Semiclassical analysis of quasiexact solvability

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 55, Issue 4, 1997, Pages 2625-2629

  Bender, Carl M ^a   Dunne, Gerald V ^b   Moshe, Moshe ^c  

^a WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000234540     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.55.2625     Document Type: Article

References (16)

1. See A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (Institute of Physics, Bristol, 1993), and references therein.
2. A. V. Turbiner, Zh. Éksp. Teor. Fiz. 67, 230 (1988) [Sov. Phys. JETP 67, 230 (1988)];
3. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988);
4. A. V. Turbiner, Contemp. Math. 160, 263 (1994);
5. M. A. Shifman, Contemp. Math.ibid. 160, 237 (1994).
6. M. A. Shifman and A. V. Turbiner, Commun. Math. Phys. 126, 347 (1989).
7. A. González-López, N. Kamran and P. J. Olver, Commun. Math. Phys. 153, 117 (1993); Contemp. Math. 160, 113 (1994).
8. F. Iachello, Nucl. Phys. A560, 23 (1993);
9. F. Iachello, Contemp. Math. 160, 151 (1994).
10. see C. M. Bender and G. V. Dunne, J. Math. Phys. 37, 6 (1996). This property extends to other QES potentials;A. Krajewska, A. Ushveridze, and Z. Walczak (unpublished); F. Finkel, A. González-López, and M. A. Rodríguez (unpublished).
11. For the polynomial potentials in this paper V(x)∼(Formula presented)(J) (J→∞) at (complex) points where (Formula presented)(x)=0.
12. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 8.
13. C. M. Bender and S. A. Orszag, (Ref. 8), Chap. 10.
14. F. T. Hioe and E. W. Montroll, J. Math. Phys. 16, 1945 (1975);
15. F. T. Hioe, D. MacMillen and E. W. Montroll, J. Math. Phys. 17, 1320 (1976).
16. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, D.C., 1970), Chap. 15.